Some cardinal characteristics related to the covering number and the uniformity of the meagre ideal

• Autorzy: Sonpanow Nattapon , Vejjajiva Pimpen

Identyfikatory

DOI

:10.4467/20842589RM.21.006.14373

• Języki publikacji: EN

Abstrakty

EN

We extend the concepts of splitting, reaping, and independent families to families of functions and permutations on ω and define associated cardinal characteristics sf , sp, rf , rp, if , and ip. We study relationships among cov(M), non(M), and these cardinals. In this paper, we show that sf = non(M) = sp, rf = cov(M) ≤ rp, and cov(M) ≤ if , ip.

Słowa kluczowe

EN

cardinal characteristic; covering number; uniformity

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2021
• Tom: Vol. 56
• Strony: 3--14
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Sonpanow Nattapon

• Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok 10330, Thailand

autor

Vejjajiva Pimpen

• Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok 10330, Thailand

Bibliografia

• [1] T. Bartoszyński, Combinatorial aspects of measure and category, Fundamenta Mathematicae, 127 (1987), 225–239.
• [2] M. G. Bell, On the combinatorial principle P(c), Fundamenta Mathematicae, 114 (1981), 149–157.
• [3] A. Blass, Combinatorial cardinal characteristics of the continuum, In: Handbook of Set Theory, vol. 1, M. Foreman, A. Kanamori (eds.), (Springer, Berlin, 2010), 395–490.
• [4] J. Brendle, O. Spinas, Y. Zhang, Uniformity of the meager ideal and maximal cofinitary groups, Journal of Algebra, 232 (2000), 209–225.
• [5] D. H. Fremlin, S. Shelah, On partitions of the real line, Israel Journal of Mathematics, 32 (1979), 299–304.
• [6] L. J. Halbeisen, Combinatorial set theory: With a gentle introduction to forcing, 2 ed., Springer International Publishing (2017).
• [7] K. Kunen, Set theory, vol. 34 of Studies in logic, College Publications (2011).
• [8] N. Sonpanow, P. Vejjajiva, Independent families of functions and permutations, Mathematical Logic Quarterly, 66 (2020), 311–315.
• [9] Y. Zhang, On a class of m.a.d. families, Journal of Symbolic Logic, 64 (1999), 737–746.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).